Question

Consider the following system of equations:

y = −x + 2
y = 3x + 1

Which description best describes the solution to the system of equations?

Line y = −x + 2 intersects line y = 3x + 1.
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
Line y = −x + 2 intersects the origin.

Answer 1

y = -x + 2
y = 3x + 1

-x + 2 = 3x + 1
+ x + x
2 = 4x + 1
- 1 - 1
1 = 4x
4 4
¹/₄ = x

y = 3x + 1
y = 3(¹/₄) + 1
y = ³/₄ + 1
y = 1³/₄
(x, y) = (¹/₄, 1³/₄)

The answer is A.

Answer 2

The correct option is A. Line y = −x + 2 intersects line y = 3x + 1.

Explanation:

The first equation is given to be :

y = -x + 2

x 0 2

y 2 0

The second equation is :

y = 3x + 1

x 0 -1/3

y 1 0

Now, The graphs of both the equation are attached below :

So, By seeing the graph, We can observe :

• Line y = −x + 2 intersects line y = 3x + 1.

• Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.

• Lines y = −x + 2 and y = 3x + 1 intersect the y-axis

But the description that best describes the solution to the system of equations is : Line y = −x + 2 intersects line y = 3x + 1.

Hence, The correct option is A. Line y = −x + 2 intersects line y = 3x + 1.